A novel statistical workflow for nonstationary modelling of successive Fr\'{e}chet extremes

Abstract

Accurate estimation of the frequency and magnitude of successive extreme events in energy demand is critical for strategic resource planning. Traditional approaches based on extreme value theory (EVT) are typically limited to modelling isolated extreme events and struggle to capture the dynamics of temporally clustered extremes, such as those driven by prolonged extreme weather events. These limitations are exacerbated by the scarcity of historical data and computational costs of longrun simulations leading to high uncertainty in return level estimates for successive extremes. Here, we introduce a novel statistical framework leveraging recent theoretical advances in successive extreme value modelling in dynamical systems. Under reasonable assumptions of the time series data (e.g. the data follow a fat-tailed Fr\'{e}chet distribution), our tool allows for significantly more robust estimates of returns and magnitudes of successive extreme events compared to standard likelihood methods. We illustrate our statistical workflow on scenarios of forecasted gas supply levels from 2025 to 2050. Common measures of statistical accuracy are provided as benchmarks for comparison.